The interesting history protrayed has to do with the Emancipation Proclamation. The two members of the Cabinet on Lincoln's right (viewer's left) supported Lincoln's initial draft. The five cabinet members to Lincoln's left did not initially support the Emancipation Proclamation. All except Bates, the Atty. Gen. (far right of portrait) more or less came around.
His replacement for Secretary of War, Edwin Stanton, was not only a staunch Democrat, but a supporter of the secessionist candidate, i.e., Breckrinridge, in the pivotal 1860 presidential election, illustrates this fact more vividly than any other.
Combine this with Lincoln's choice of a border state Whig/Republican, i.e., Bates, for Attorney General, and his choice of a moderate antislavery senator and chief rival for the Rep. nomination, William Seward, for Sec'y of State, and it's hard to believe that anyone would accuse President Lincoln of being some sort of dogmatic, unyielding ideologue.